While some of the inherent deficiencies of the basic ABC algorithm are hard to tackle, one can significantly improve the sampling process by which candidates \(\theta _i\)  are drawn from \(p(\theta )\) . Various more sophisticated ABC algorithms have been proposed such as those based on Markov chain Monte Carlo chains  or particle filters , [1]} (sequential Monte Carlo). For our analysis we opted to use an ABC sequential Monte Carlo (SMC) algorithm for which we will explain the implementation in detail in the next section.
